Finite Group Databasebeta

← C2×#11741126 #14234812

Subgroups — C2×#11741126 #14234812

Order 1792.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#556C211yesmaximal, characteristic, complemented
2C2×#90275C211yesmaximal, characteristic, complemented
3#11741126C2116yesmaximal, direct product factor
4C2×#89862C211yesmaximal, characteristic, complemented
5C2×#89858C211yesmaximal, characteristic, complemented
6C2×#89826C211yesmaximal, characteristic, complemented
7C2×#89829C211yesmaximal, characteristic
8C2×#89832C211yesmaximal, characteristic, complemented
9C2×#89831C211yesmaximal, characteristic
10C2×#89803C211yesmaximal, characteristic, complemented
11C2×#89800C211yesmaximal, characteristic, complemented
12C2×#89798C211yesmaximal, characteristic, complemented
13C2×#89796C211yesmaximal, characteristic, complemented
14C2×C4×#1144C211yesmaximal, characteristic, complemented
15C2×#89788C211yesmaximal, characteristic
16C2×#89790C211yesmaximal, characteristic, complemented
17C7×#556—24no—
18C7×#556C2218yescomplemented
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#126—21no—
21C2×C7×#126—21no—
22C2×C7×#124C2211yescharacteristic
23C2×C7×#124C2211yescharacteristic
24C2×C7×C22⋊Q8—21no—
25C2×C4×C7×Q8C2211yescharacteristic
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×Q8C2211yescharacteristic
28C2×C4×C7×D4C2211yescharacteristic
29C2×C7×#117—21no—
30C2×#6509—21no—
31C22×#1144C2211yescharacteristic
32C22×#1144C2211yescharacteristic
33C22×#1144C2211yescharacteristic
34C22×#1144C2211yescharacteristic
35C22×#1143C2211yescharacteristic
36C22×#1143C2211yescharacteristic
37C22×#1142C2211yescharacteristic
38C22×#1142C2211yescharacteristic
39C22×#1141C2211yescharacteristic
40#90275—24no—
41#90275C2218yescomplemented
42C2×#6461—21no—
43C2×#6461—21no—
44C2×#6455—21no—
45C2×#6438C2211yescharacteristic
46C2×#6438C2211yescharacteristic
47C2×C4×D28C2211yescharacteristic
48C2×#6432C2211yescharacteristic
49C2×C4×Dic14C2211yescharacteristic
50C2×C4×Dic14C2211yescharacteristic
51C2×#6409C2211yescharacteristic
52C2×#6409C2211yescharacteristic
53C2×#6406C2211yescharacteristic
54#89862C2218yescomplemented
55#89858C2218yescomplemented
56#89832C2218yescomplemented
57#89831C2218yes—
58#89829C2218yes—
59#89826C2218yescomplemented
60#89803C2218yescomplemented
61C4×#1144C2218yescomplemented
62#89800C2218yescomplemented
63#89798C2218yescomplemented
64#89796C2218yescomplemented
65#89790C2218yescomplemented
66#89788C2218yes—
67C2×#6384C2211yescharacteristic
68C2×#6384C2211yescharacteristic
69C2×#6383C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×C4⋊(C7⋊C8)C2211yescharacteristic
72C2×C4⋊(C7⋊C8)C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×#6377C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3402—71nomaximal, Sylow
78C22×C7×Q8D411yescharacteristic
79C22×C7×Q8C2311yescharacteristic
80C22×C7×Q8C2311yescharacteristic
81C22×C7×D4C2311yescharacteristic
82C23×C4×C7—21no—
83C22×D28C2311yescharacteristic
84C22×C4×D7—21no—
85C22×Dic14C2311yescharacteristic
86C22×Dic14C2311yescharacteristic
87C7×C4⋊Q8—22no—
88C7×C4⋊Q8C2314yes—
89C7×#126—28no—
90C7×#126—28no—
91C7×#124—22no—
92C7×#124—22no—
93C7×#124C2314yes—
94C7×#124C2314yes—
95C7×C22⋊Q8—28no—
96C4×C7×Q8—22no—
97C4×C7×Q8—22no—
98C4×C7×Q8D414yes—
99C4×C7×Q8C2314yes—
100C4×C7×Q8C2314yes—
101C4×C7×Q8C2314yes—
102C4×C7×D4—22no—
103C4×C7×D4C2314yes—
104C7×#117—28no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—21no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4D411yescharacteristic
110C2×C7×C4⋊C4D411yescharacteristic
111C2×C7×C4⋊C4D411yescharacteristic
112C2×C7×C4⋊C4C2311yescharacteristic
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4—21no—
116C2×C7×C22⋊C4—21no—
117C2×C7×C22⋊C4—21no—
118C2×C42×C7—21no—
119C2×C42×C7—21no—
120C2×C42×C7C2311yescharacteristic
121C2×C42×C7C2311yescharacteristic
122C2×C42×C7C2311yescharacteristic
123#6509—28no—
124C2×#1144—24no—
125C2×#1144—42no—
126C2×#1144—42no—
127C2×#1144—42no—
128C2×#1144C2314yes—
129C2×#1144C2314yes—
130C2×#1144C2314yes—
131C2×#1144C2314yes—
132C2×#1143—24no—
133C2×#1143—42no—
134C2×#1143C2314yes—
135C2×#1143C2314yes—
136C2×#1142—24no—
137C2×#1142—42no—
138C2×#1142C2314yes—
139C2×#1142C2314yes—
140C2×#1141—42no—
141C2×#1141C2314yes—
142C2×(C2×D7)⋊C4—21no—
143C2×(C2×D7)⋊C4—21no—
144C2×(C2×D7)⋊C4—21no—
145C2×(C2×D7)⋊C4—21no—
146C2×(C2×D7)⋊C4—21no—
147C2×C4⋊Dic7—21no—
148C2×C4⋊Dic7—21no—
149C2×C4⋊Dic7C2311yescharacteristic
150C2×Dic7⋊C4—21no—
151C2×Dic7⋊C4—21no—
152C2×C4×Dic7—21no—
153C2×C4×Dic7—21no—
154C22×C7⋊C8C2311yescharacteristic
155C22×C7⋊C8C2311yescharacteristic
156C22×C7⋊C8C2311yescharacteristic
157C22×C7⋊C8C2311yescharacteristic
158#6461—28no—
159#6461—28no—
160#6455—28no—
161#6438—22no—
162#6438—22no—
163#6438C2314yes—
164#6438C2314yes—
165C4×D28—22no—
166C4×D28C2314yes—
167#6432—22no—
168#6432C2314yes—
169C4×Dic14—22no—
170C4×Dic14—22no—
171C4×Dic14C2314yes—
172C4×Dic14C2314yes—
173#6409C2314yes—
174#6409C2314yes—
175#6406C2314yes—
176#6384C2314yes—
177#6384C2314yes—
178#6383C2314yes—
179#6381C2314yes—
180C4⋊(C7⋊C8)C2314yes—
181C4⋊(C7⋊C8)C2314yes—
182C4⋊(C7⋊C8)C2314yes—
183#6377C2314yes—
184#6377C2314yes—
185C4×C7⋊C8C2314yes—
186C2×#556—71no—
187C2×#556D711yescharacteristic, complemented
188#3402—716no—
189C2×#497—71no—
190C2×#497—71no—
191C2×#495—71no—
192C2×#464—71no—
193C2×#464—71no—
194C2×#462—71no—
195C2×#462—71no—
196C2×#463—71no—
197C2×#463—71no—
198C2×#446—71no—
199C2×#440—71no—
200C2×#440—71no—
201C2×C4×Q16—71no—
202C24×C7—21no—
203C23×D7—21no—
204C2×C7×Q8—21no—
205C2×C7×Q8—21no—
206C2×C7×Q8—22no—
207C2×C7×Q8—22no—
208C2×C7×Q8—22no—
209C2×C7×Q8—22no—
210C2×C7×Q8—42no—
211C2×C7×Q8C2×D414yes—
212C2×C7×Q8C2412yes—
213C2×C7×Q8C2412yes—
214C2×C7×D4—21no—
215C2×C7×D4—22no—
216C2×C7×D4—22no—
217C2×C7×D4C2412yes—
218C22×C4×C7—21no—
219C22×C4×C7—21no—
220C22×C4×C7—21no—
221C22×C4×C7—24no—
222C22×C4×C7—44no—
223C22×C4×C7C2×D411yescharacteristic
224C22×C4×C7C2×D411yescharacteristic
225C22×C4×C7C2×D411yescharacteristic
226C22×C4×C7C2×D411yescharacteristic
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D411yescharacteristic
229C22×C4×C7C2411yescharacteristic
230C22×Dic7—21no—
231C22×Dic7—21no—
232C22×Dic7—21no—
233C2×D28—22no—
234C2×D28—22no—
235C2×D28—21no—
236C2×D28C2412yes—
237C2×C4×D7—24no—
238C2×C4×D7—44no—
239C2×Dic14—22no—
240C2×Dic14—22no—
241C2×Dic14—22no—
242C2×Dic14—22no—
243C2×Dic14—21no—
244C2×Dic14—21no—
245C2×Dic14C2412yes—
246C2×Dic14C2412yes—
247C7×C4⋊C4—24no—
248C7×C4⋊C4—24no—
249C7×C4⋊C4—24no—
250C7×C4⋊C4—24no—
251C7×C4⋊C4—21no—
252C7×C4⋊C4C2×D414yes—
253C7×C4⋊C4C2×D414yes—
254C7×C4⋊C4C2×D414yes—
255C7×C4⋊C4C2412yes—
256C7×C22⋊C4—24no—
257C7×C22⋊C4—24no—
258C7×C22⋊C4—24no—
259C7×C22⋊C4—24no—
260C7×C22⋊C4—24no—
261C42×C7—24no—
262C42×C7—24no—
263C42×C7C2×D412yes—
264C42×C7C2×D412yes—
265C42×C7C2×D412yes—
266C42×C7C2412yes—
267C42×C7C2412yes—
268C42×C7C2412yes—
269#1144—28no—
270#1144—44no—
271#1144—44no—
272#1144—44no—
273#1143—28no—
274#1143—44no—
275#1142—28no—
276#1142—44no—
277#1141—44no—
278(C2×D7)⋊C4—24no—
279(C2×D7)⋊C4—24no—
280(C2×D7)⋊C4—24no—
281(C2×D7)⋊C4—24no—
282(C2×D7)⋊C4—24no—
283C4⋊Dic7—21no—
284C4⋊Dic7—24no—
285C4⋊Dic7—24no—
286C4⋊Dic7C2412yes—
287Dic7⋊C4—24no—
288Dic7⋊C4—24no—
289C4×Dic7—24no—
290C4×Dic7—24no—
291C2×C7⋊C8—22no—
292C2×C7⋊C8—22no—
293C2×C7⋊C8—22no—
294C2×C7⋊C8#4114yes—
295C2×C7⋊C8C2412yes—
296C2×C7⋊C8C2412yes—
297C2×C7⋊C8C2412yes—
298C2×C7⋊C8C2412yes—
299C22×Q16—71no—
300C22×Q16—71no—
301C22×Q16—71no—
302C22×Q16—71no—
303C22×SD16—71no—
304C22×SD16—71no—
305C22×SD16—71no—
306C22×SD16—71no—
307C22×D8—71no—
308#556—24no—
309#556—78no—
310#556—144no—
311#556C2×D718yescomplemented
312C2×C4⋊Q8—71no—
313C2×C4⋊Q8C2×D711yescharacteristic
314C2×#126—21no—
315C2×#126—21no—
316C2×#126—141no—
317C2×#126—141no—
318C2×#124—71no—
319C2×#124—71no—
320C2×#124C2×D711yescharacteristic
321C2×#124C2×D711yescharacteristic
322C2×C22⋊Q8—21no—
323C2×C22⋊Q8—141no—
324C2×C4×Q8—71no—
325C2×C4×Q8—71no—
326C2×C4×Q8C2×D711yescharacteristic
327C2×C4×Q8C2×D711yescharacteristic
328C2×C4×Q8C2×D711yescharacteristic
329C2×C4×D4—71no—
330C2×C4×D4C2×D711yescharacteristic
331C2×#117—21no—
332C2×#117—141no—
333#497—78no—
334#497—78no—
335#495—78no—
336#464—78no—
337#464—78no—
338#463—78no—
339#463—78no—
340#462—78no—
341#462—78no—
342#446—78no—
343#440—78no—
344#440—78no—
345C4×Q16—78no—
346C2×#107—71no—
347C2×C4⋊C8—71no—
348C2×C4⋊C8—71no—
349C2×C4⋊C8—71no—
350C2×#103—71no—
351C2×#103—71no—
352C2×#103—71no—
353C2×#103—71no—
354C2×#102—71no—
355C2×#102—71no—
356C2×#97—71no—
357C2×#97—71no—
358C2×C4×C8—71no—
359C23×C7—22no—
360C23×C7—42no—
361C23×C7—42no—
362C23×C7—42no—
363C23×C7C22×D411yescharacteristic
364C22×D7—22no—
365C22×D7—42no—
366C22×D7—42no—
367C22×D7—42no—
368C7×Q8—22no—
369C7×Q8—22no—
370C7×Q8—22no—
371C7×Q8—22no—
372C7×Q8—44no—
373C7×Q8—42no—
374C7×Q8—42no—
375C7×D4—22no—
376C7×D4—22no—
377C7×D4—42no—
378C2×C4×C7—22no—
379C2×C4×C7—22no—
380C2×C4×C7—22no—
381C2×C4×C7—22no—
382C2×C4×C7—22no—
383C2×C4×C7—22no—
384C2×C4×C7—22no—
385C2×C4×C7—22no—
386C2×C4×C7—22no—
387C2×C4×C7—48no—
388C2×C4×C7—42no—
389C2×C4×C7—42no—
390C2×C4×C7—42no—
391C2×C4×C7C22×D412yes—
392C2×C4×C7C22×D412yes—
393C2×C4×C7C22×D412yes—
394C2×C4×C7C22×D412yes—
395C2×C4×C7C22×D412yes—
396C2×C4×C7C22×D412yes—
397C2×C4×C7C22×D411yescharacteristic
398C2×C4×C7C2×#4112yes—
399C2×C4×C7H(5,𝔽2)12yes—
400C2×C4×C7C2511yescharacteristic
401C2×Dic7—22no—
402C2×Dic7—22no—
403C2×Dic7—22no—
404C2×Dic7—42no—
405C2×Dic7—42no—
406C2×Dic7—42no—
407D28—22no—
408D28—22no—
409D28—42no—
410C4×D7—48no—
411Dic14—22no—
412Dic14—22no—
413Dic14—22no—
414Dic14—22no—
415Dic14—42no—
416Dic14—42no—
417C7⋊C8—22no—
418C7⋊C8—22no—
419C7⋊C8—22no—
420C7⋊C8C2×#4114yes—
421C22×Q8—71no—
422C22×Q8—71no—
423C22×Q8C22⋊D711yescharacteristic
424C22×Q8C22×D711yescharacteristic
425C22×Q8C22×D711yescharacteristic
426C22×D4—71no—
427C22×D4C22×D711yescharacteristic
428C23×C4—21no—
429C23×C4—141no—
430C2×Q16—74no—
431C2×Q16—74no—
432C2×Q16—74no—
433C2×Q16—74no—
434C2×Q16—144no—
435C2×Q16—282no—
436C2×Q16—282no—
437C2×Q16—282no—
438C2×SD16—74no—
439C2×SD16—74no—
440C2×SD16—74no—
441C2×SD16—74no—
442C2×SD16—144no—
443C2×SD16—144no—
444C2×SD16—282no—
445C2×SD16—282no—
446C2×D8—74no—
447C2×D8—282no—
448C22×C8—71no—
449C22×C8—71no—
450C22×C8—71no—
451C22×C8—71no—
452C4⋊Q8—22no—
453C4⋊Q8—74no—
454C4⋊Q8—142no—
455C4⋊Q8C22×D714yes—
456#126—28no—
457#126—28no—
458#126—148no—
459#126—148no—
460#124—22no—
461#124—22no—
462#124—74no—
463#124—74no—
464#124—142no—
465#124—142no—
466#124C22×D714yes—
467#124C22×D714yes—
468C22⋊Q8—28no—
469C22⋊Q8—148no—
470C4×Q8—22no—
471C4×Q8—22no—
472C4×Q8—74no—
473C4×Q8—74no—
474C4×Q8—142no—
475C4×Q8—142no—
476C4×Q8C22⋊D714yes—
477C4×Q8C22×D714yes—
478C4×Q8C22×D714yes—
479C4×Q8C22×D714yes—
480C4×D4—22no—
481C4×D4—74no—
482C4×D4—142no—
483C4×D4C22×D714yes—
484#117—28no—
485#117—148no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—71no—
491C2×C4⋊C4—141no—
492C2×C4⋊C4—141no—
493C2×C4⋊C4—141no—
494C2×C4⋊C4—141no—
495C2×C4⋊C4C22⋊D711yescharacteristic
496C2×C4⋊C4C22⋊D711yescharacteristic
497C2×C4⋊C4C22⋊D711yescharacteristic
498C2×C4⋊C4C22×D711yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—141no—
505C2×C22⋊C4—141no—
506C2×C22⋊C4—141no—
507C2×C22⋊C4—141no—
508C2×C22⋊C4—141no—
509C2×C42—21no—
510C2×C42—21no—
511C2×C42—141no—
512C2×C42—141no—
513C2×C42C22×D711yescharacteristic
514C2×C42C22×D711yescharacteristic
515C2×C42C22×D711yescharacteristic
516#107—74no—
517C4⋊C8—74no—
518C4⋊C8—74no—
519C4⋊C8—74no—
520#103—74no—
521#103—74no—
522#103—74no—
523#103—74no—
524#102—74no—
525#102—74no—
526#97—74no—
527#97—74no—
528C4×C8—74no—
529C22×C7—42no—
530C22×C7—42no—
531C22×C7—42no—
532C22×C7—84no—
533C22×C7#55012yes—
534C22×C7#57512yes—
535C22×C7#57812yes—
536C22×C7C23×D411yescharacteristic
537C2×D7—42no—
538C2×D7—42no—
539C2×D7—42no—
540C2×D7—84no—
541C4×C7—22no—
542C4×C7—22no—
543C4×C7—22no—
544C4×C7—22no—
545C4×C7—22no—
546C4×C7—22no—
547C4×C7—42no—
548C4×C7—42no—
549C4×C7—42no—
550C4×C7#55012yes—
551C4×C7C22×#4111yescharacteristic
552C4×C7C2×H(5,𝔽2)11yescharacteristic
553Dic7—42no—
554Dic7—42no—
555Dic7—42no—
556C24—21no—
557C24—141no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—22no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—42no—
565C2×Q8—72no—
566C2×Q8—72no—
567C2×Q8—141no—
568C2×Q8—141no—
569C2×Q8—142no—
570C2×Q8—142no—
571C2×Q8—142no—
572C2×Q8—142no—
573C2×Q8C2×C22⋊D714yes—
574C2×Q8C23×D712yes—
575C2×Q8C23×D712yes—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—72no—
580C2×D4—142no—
581C2×D4—142no—
582C2×D4—141no—
583C2×D4C23×D712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—141no—
590C22×C4—141no—
591C22×C4—141no—
592C22×C4—144no—
593C22×C4—284no—
594C22×C4C2×C22⋊D711yescharacteristic
595C22×C4C2×C22⋊D711yescharacteristic
596C22×C4C2×C22⋊D711yescharacteristic
597C22×C4C2×C22⋊D711yescharacteristic
598C22×C4C2×C22⋊D711yescharacteristic
599C22×C4C2×C22⋊D711yescharacteristic
600C22×C4C23×D711yescharacteristic
601Q16—148no—
602Q16—284no—
603Q16—284no—
604Q16—284no—
605SD16—148no—
606SD16—148no—
607SD16—284no—
608SD16—284no—
609D8—284no—
610C2×C8—74no—
611C2×C8—72no—
612C2×C8—72no—
613C2×C8—72no—
614C2×C8—72no—
615C2×C8—142no—
616C2×C8—142no—
617C2×C8—142no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—72no—
624C4⋊C4—144no—
625C4⋊C4—144no—
626C4⋊C4—141no—
627C4⋊C4—144no—
628C4⋊C4—144no—
629C4⋊C4C2×C22⋊D714yes—
630C4⋊C4C2×C22⋊D714yes—
631C4⋊C4C2×C22⋊D714yes—
632C4⋊C4C23×D712yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—144no—
639C22⋊C4—144no—
640C22⋊C4—144no—
641C22⋊C4—144no—
642C22⋊C4—144no—
643C42—24no—
644C42—24no—
645C42—144no—
646C42—144no—
647C42C2×C22⋊D712yes—
648C42C2×C22⋊D712yes—
649C42C2×C22⋊D712yes—
650C42C23×D712yes—
651C42C23×D712yes—
652C42C23×D712yes—
653C2×C7—82no—
654C2×C7#340214yescomplemented
655C2×C7C2×#55011yescharacteristic
656C2×C7C2×#57511yescharacteristic
657C2×C7C2×#57811yescharacteristic
658D7—82no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—142no—
664C23—282no—
665C23—282no—
666C23—282no—
667C23C22×C22⋊D711yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—44no—
673Q8—42no—
674Q8—42no—
675Q8—142no—
676Q8—142no—
677Q8—142no—
678Q8—142no—
679Q8—282no—
680Q8—282no—
681D4—22no—
682D4—22no—
683D4—42no—
684D4—142no—
685D4—142no—
686D4—282no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—142no—
701C2×C4—142no—
702C2×C4—142no—
703C2×C4—288no—
704C2×C4—282no—
705C2×C4—282no—
706C2×C4—282no—
707C2×C4D7×#4112yes—
708C2×C4#655312yes—
709C2×C4C22×C22⋊D712yes—
710C2×C4C22×C22⋊D712yes—
711C2×C4C22×C22⋊D712yes—
712C2×C4C22×C22⋊D712yes—
713C2×C4C22×C22⋊D712yes—
714C2×C4C22×C22⋊D712yes—
715C2×C4C22×C22⋊D711yescharacteristic
716C2×C4C24×D711yescharacteristic
717C8—74no—
718C8—142no—
719C8—142no—
720C8—142no—
721C7C2×#340211yescharacteristic, complemented, Sylow
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—282no—
727C22—282no—
728C22—282no—
729C22—564no—
730C22#9051312yes—
731C22#9052512yes—
732C22#9052912yes—
733C22C23×C22⋊D711yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—282no—
744C4—282no—
745C4—282no—
746C4#9052512yes—
747C4C2×D7×#4111yescharacteristic
748C4C2×#655311yescharacteristic
749C2—82no—
750C2—562no—
751C2#1174112614yesdirect product factor
752C2C2×#9051311yescharacteristic
753C2C2×#9052511yescharacteristic
754C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#556C2
socleC23×C7C22×D4
prime radicalC22×#1141C22
hypercenterC2×#556D7
hypocenterC7C2×#3402
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C7×#556C2semidirect
2. C2×#90275C2semidirect
3. #11741126C2direct (N × H)
4. C2×#89862C2semidirect
5. C2×#89858C2semidirect
6. C2×#89826C2semidirect
8. C2×#89832C2semidirect
10. C2×#89803C2semidirect
11. C2×#89800C2semidirect
12. C2×#89798C2semidirect
13. C2×#89796C2semidirect
14. C2×C4×#1144C2semidirect
16. C2×#89790C2semidirect
18. C7×#556C22semidirect
41. #90275C22semidirect
54. #89862C22semidirect
55. #89858C22semidirect
56. #89832C22semidirect
59. #89826C22semidirect
60. #89803C22semidirect
61. C4×#1144C22semidirect
62. #89800C22semidirect
63. #89798C22semidirect
64. #89796C22semidirect
65. #89790C22semidirect
187. C2×#556D7semidirect
311. #556C2×D7semidirect
654. C2×C7#3402semidirect
721. C7C2×#3402semidirect
751. C2#11741126direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#5562
C2×#902752
#117411262
C2×#898622
C2×#898582
C2×#898262
C2×#898292
C2×#898322
C2×#898312
C2×#898032
C2×#898002
C2×#897982
C2×#897962
C2×C4×#11442
C2×#897882
C2×#897902
C2×#34027